Transverse Elements

We shall next investigate the transverse case, in particular where the line array is oriented in the x direction d the reference element located at R (0,0, zO while the point of observation is R(x,y,z), as shown in Fig. 3.4. 

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In the [ 45]j tensile test (ASTM D 3518,1991) shown in Fig 3.22, a uniaxial tension is applied to a ( 45°) laminate symmetric about the mid-plane to measure the strains in the longitudinal and transverse directions, and Ey. This can be accomplished by instrumenting the specimen with longitudinal and transverse element strain gauges. Therefore, the shear stress-strain relationships can be calculated from the tabulated values of and Ey, corresponding to particular values of longitudinal load, (or stress relations derived from laminated plate theory (Petit, 1969 Rosen, 1972) ... 

Since E ix ) = 0 at the endpoints of the reference dement, the first term in (3.45) must equal zero. Thus, the total y component at 7J(.v, y, z) of the field from the line array with transverse elements is... 

In this chapter we have obtained the E field from stick arrays composed of longitudinal or transverse elements of arbitrary length 21. 

For the mntual impedance between an array of transverse elements and an external orthogonal element we found that a numerical double integration was necessary. 

A stick array with transverse elements as shown in Fig. 3.4 has the interelement spacing = 0.8 cm and the reference element located at the origin. The total length of the elements are 21 = 1.5 cm, and the wire radius a is... 

Periodic structures of finite extent are often analyzed by dividing them into infinitely long column arrays (stick arrays) with either longitudinal or transverse elements. Thus, in Chapter 3 we examined both of these types of arrays in some detail. 

Fig. 8.2a-e. The pattern of a fracture is determined by the forces applied to produce it. a Spiral fracture is the result of twisting/torsional forces, b Oblique fracture due to compressive forces, c Oblique fracture (with small transverse element) due to the bone being held fast and an uneven bending force applied distal to the fracture, d Transverse fracture due to bending force about a fulcrum, e-a Butterfly fragment due to compression and bending forces... 

Oblique fractures result from shear stresses, secondary to axial loading. Pure oblique fractures, however, are rare and, more commonly, there is a minor transverse element to the fracture (Fig. 8.4). Such injuries are due to uneven bending. The middle and distal or proximal end of the bone are fixed and the free end is moved. 

This is a typical efficient measure to reduce the effect of thrust. The technique was applied in masonry structures either during construction or as a remedial measure during previous interventions (Fig. 31). The technique consists in providing at the base of the curved element horizontal ties that can sustain the horizontal component of the thrust. The ties (made of steel or stainless steel or titanium, depending on the case) are anchored to transverse elements. For the maximum acceptable stress in the ties, as well as for their anchorage to masonry, the rules presented in section Improving the Connection Between Walls are valid. 

Figure 14.3. High-magnification views of organelles from cells prepared by HPF-FS. (a) Microfilaments (arrow) in cross section. Bar, 50 nm. (b) Microfilaments in longitudinal section. The arrows point out areas of apparent transverse elements in the bundle. Bar, 50 nm. (c) Membranes between adjacent cells in a postgastrulation embryo. Bar, 200 nm. (d) Membranes between cells in a pregastrulation embryo. Bar, 200 nm. (e-g) Centrioles from syncytial blastoderm mitotic spindle poles. Bars (e) 200 nm (f,g) 100 nm. See text for additional details.

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

Unnecessary loading of the breakdown fuse through transient overvoltages can be avoided by connection to a r element which consists of a length choke and transverse capacitors. So-called iron core chokes are most conveniently used for series chokes, which are usual in power electronics. A damping element with a 61-fjF capacitor is advised at the input and output of the r element. 

In hardwoods, morphological structural elements in longitudinal series comprise the segmented structure termed vessel . Vessels, which are exposed in transverse section, constitute about 10-46% of the stem volume in deciduous hardwoods and are cells of relatively large diameters (50-300 p.m). Vessels have in short the appearance of open vertical tubes within the wood structure because their end walls have partially dissolved. By comparison, the hardwood vessel diameter can be as much a 10 times the diameter of a softwood fiber. 

A psychrometer measures the dry-bulb and wet-bulb temperatures simultaneously. The measurement of the wet-bulb temperature is achieved by means of a wet wick placed over the thermometer bulb. The thermometer can be practically of any type. A cylindrically shaped sensor is preferred. The wet-bulb temperaturesensing element, covered with the wick, and the dry-bulb temperature sensor, are placed in the airstream to be measured. The stream, generated by a small fan, should have a velocity of 3-5 m s and can be either transverse or axial. The... 

The apparent Young s modulus, E2, of the composite material in the direction transverse to the fibers is considered next. In the mechanics of materials approach, the same transverse stress, 02, is assumed to be applied to both the fiber and the matrix as in Figure 3-9. That is, equilibrium of adjacent elements in the composite material (fibers and matrix) must occur (certainly plausible). However, we cannot make any plausible approximation or assumption about the strains in the fiber and in the matrix in the 2-direction. 

REPRESENTATIVE EXTENSION MODE VOLUME ELEMENT OR TRANSVERSE MODE a b... 

Another issue that turns out to be very important for the sandwich-blade stiffener, but not at all important for the hat-shaped stiffener, is shear in the vertical web. Not shear in the plane of the web, but shear in the plane perpendicular to the web. This transverse shear stiffness turns out to dominate the behavior or be very important in the behavior of the sandwich blade, but simply is not addressed at all in the hatshaped stiffener. You can imagine that the transverse shearing stiffness would be more important in the sandwich blade when you consider the observation that the sandwich blade is a thick element and the hatshaped stiffener is a thin element. That is, bending and in-plane shear would dominate this response, whereas transverse shear, because the sandwich blade is thick, can very easily be an important factor in the sandwich blade. For both stiffeners, appropriate analyses and design rationale have been developed to be able to make an optimally shaped stiffener. 

The simplest situation is one in which a planar substrate lacks any crystallographic structure. Then the confined fluid is homogeneous and isotropic in transverse (x,y) directions. All off-diagonal elements of T vanish, Txx = Tyy = T, and Eq. (5) simplifies to... 

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